Initial volume of water:

$V_{full} = A_b \, h = \frac{1}{4}\pi (3^2)(6)$

$V_{full} = 13.5\pi ~ \text{in.}^3$

Final volume of water after tilting

$V = \frac{1}{2}V_{full} = \frac{1}{2}(13.5\pi)$

$V = 6.75\pi ~ \text{in.}^3 = 21.206 ~ \text{in.}^3$ *answer*